\section{note of 2009.10.08}
So ultimately, it is just build a model for the two channel in many-body with BCS-like condensation.  Most straightforward is to put close channel still as the point-molecule with no change tight bounded to open-channel.  However, even that may have some subtlety. As the point-like molecule wave function (for the central mass) spread and overlap each other. And it might not be just such.   

\subsection{}
One thing maybe worthes some time is relation between the particle's own momuntum and the relative momentum between two.  It is often confusing.  In the two-body case, we talk about relative momentum most of the time.  But it is more common to talk about individual mometum in many-bpdy cases.  
